Exhaust geometry for particle grouping

ABSTRACT

An exhaust pipe ( 100 ) for a fuel burning engine including a hollow body, the body having an internal surface ( 120 ), an external surface ( 110 ), a first open end ( 130 ), a second open end ( 140 ) and a longitudinal axis, wherein the internal surface ( 120 ) is shaped to form standing cyclic wave geometry having at least 2 cycles (c). When gas containing inhalable particles ( 22 ) enters the exhaust pipe ( 100 ) through the first open end ( 130 ) and flows out of the exhaust pipe ( 100 ) through the second open end ( 140 ), a substantial amount of inhalable particles ( 22 ) are grouped to form filterable particles ( 182 ).

RELATED APPLICATION

The present application claims the benefit of U.S. provisionalapplication 61/164,477 filed on Mar. 30, 2009, the disclosure of whichis incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to clustering of small particles and moreparticularly to grouping of submicron particles in a pipe having astanding wave like geometry.

BACKGROUND AND PRIOR ART

There is a major health and environmental concern regarding emittedparticles from vehicle exhaust pipes, in particularly from Dieselengines. Particles, having a size ranging from nanometers to micrometers(herein after referred to as “submicron particles”), impose risk to thehealth and to the environment. Since the submicron particles are smallin size, it is easier for the submicron particles to penetrate therespiratory system. Furthermore, the stay time of smaller size particlesin the air is much longer. For example, a particle of 0.1 micron willstay about 100 times longer in the air than a particle of 1 micron.Hence, submicron particles impose a two-fold risk: (a) longer exposureand (b) easier penetration to the lungs. This risk is described innumerous academic papers as well as in the US-EPA website. Emittedparticles also harm vegetation and even the surface of buildings andmonuments. The term “inhaleable particles” is used hereininterchangeably with the term “submicron particles”.

Hence, increasing a particle's size at the expense of reducing thenumber of submicron particles will reduce the above mentioned riskimpose by submicron particles to the health and environment. The term“filterable particles” as used herein refer to particles large enoughsuch that inhaling organisms of living subjects in general, and those ofhuman beings in particular, are capable of filtering the filterableparticles, thereby preventing filterable particles from entering thelungs. Filterable particles also correspond to particles which can becaptured by a mechanical filter.

The grouping of submicron particles brings to coagulation and to theformation of larger size particles and thereby decrease the number ofsubmicron particles. There is therefore a need and it would beadvantageous to have an apparatus that groups submicron particles intolarger size particles, preferably filterable particles, and therebydecrease the number of submicron particles, for example, submicronparticles departing from the exhaust system of an engine such as aDiesel engine.

A mathematical analysis concerning the grouping of submicron particles,by D. Katoshevski, “Characteristics of Spray Grouping/Non-GroupingBehavior”, Aerosol and Air Quality Research, Vol. 6 (1), pp. 54-66, 2006is incorporated by reference for all purposes as if fully set forthherein. The analysis shows that when the velocity of the matter carryingthe submicron particles, such as air, has a form of a moving wave,particles that are carried by such a wave may form groups under specificrange of parameters. Such a wave exists in various systems such as inthe case of particles in the sea-water where the wave is moving,described in Winter, C. at al, “Grouping Dynamics of Suspended Matter inTidal Channels”, J. Geophysical Research (JGR), Vol. 112: C08010, doi:10.1029/2005JC003423, 2007, which is incorporated by reference for allpurposes as if fully set forth herein.

SUMMARY OF THE INVENTION

According to the teachings of the present invention, there is providedan exhaust pipe for a fuel burning engine including a hollow body, thebody having an internal surface, an external surface, a first open end,a second open end and a longitudinal axis, wherein the internal surfaceis shaped to form standing cyclic wave geometry having at least 2cycles.

When gas containing inhalable particles that enters the exhaust pipethrough the first open end and flows out of the exhaust pipe through thesecond open end, a substantial amount of the inhalable particles aregrouped to form filterable particles while flowing inside the exhaustpipe, whereby substantially increasing the quantity of filterableparticles and substantially reducing the quantity of inhalable.

Typically, the longitudinal axis is disposed horizontally. But invariations of the present invention, the longitudinal axis is disposedvertically, wherein the second open end is elevated with respect to thefirst open end. In other variations of the present invention, thelongitudinal axis is disposed diagonally, wherein the second open end iselevated with respect to the first open end.

Typically, the cross section of the exhaust pipe can be radial,polygonal, elliptical or other shapes.

The standing cyclic wave includes a narrow radial dimension D_(N) and awide radial dimension D_(W), wherein the narrow radial dimension D_(N)is substantially smaller than the wide radial dimension D_(W). The ratioD_(W)/D_(N) directly influences the grouping tendency of submicronparticles.

The velocity field U inside the exhaust pipe is a standing wave velocityfield, computed as follows:

U=U _(a) −U _(b) cos(kx)(sin(ωt)+C),

where U_(a) is the mean velocity, C is constant, U_(b) is the amplitude,a) is the angular frequency of the wave:

$\omega = \frac{2\pi}{T}$

where T is said wave period, and k is said wave number:

$k = \frac{2\pi}{L}$

where L is said wave length, and wherein said constant C is selected toachieve the maximal and minimal velocity values at D_(W) and D_(N),respectively.

The normalized velocity field U* is:

U*=U* _(a) −U* _(b) cos(x*)(sin(t*)+C),

where the velocities are normalized with a characteristic velocity:U_(c), where U_(c)=ω/k; x is normalized with k and t with ω, and whereinthe asterisk denotes dimensionless parameters, and wherein substantialgrouping occurs when:

$\frac{\left( {U_{a}^{*} - 1} \right)}{U_{b}^{*}} < 1.$

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become fully understood from the detaileddescription given herein below and the accompanying drawings, which aregiven by way of illustration and example only and thus not limitative ofthe present invention, and wherein:

FIG. 1 is a graphical illustrates of an example of particle trajectoriesshowing the formation of two groups;

FIG. 2 is a cross section illustration of an exhaust-pipe, according toembodiments of the present invention;

FIG. 3 a shows an example of a circular cross section of theexhaust-pipe shown in FIG. 2;

FIG. 3 b shows an example of an elliptical cross section of theexhaust-pipe shown in FIG. 2;

FIG. 4 a graphically illustrates the grouping of particles as a resultof flowing speed changes inside the exhaust-pipe shown in FIG. 2;

FIG. 4 b graphically illustrates the sinusoidal change in the particlesflow speed over time, while flowing inside the exhaust-pipe shown inFIG. 2;

FIG. 5 schematically illustrates an experimental setup having theexhaust of a Diesel engine operatively attached, in parallel, to astraight conventional steel pipe and to a cyclic exhaust pipe, accordingto embodiments of the present invention, as well as an enlargement ofone cycle of the cyclic exhaust pipe;

FIG. 6 graphically illustrates the decrease of the amount inhaleableparticles flowing out of the exhaust pipe, shown in FIG. 5, comparedwith the inhalable particles flowing out of conventional straight pipe;

FIG. 7 graphically illustrates the effect of a cyclic exhaust pipe,according to embodiments of the present invention, on the particulates'size distribution;

FIG. 8 graphically illustrates the effect of the engine's load on theparticulates' size distribution;

FIG. 9 graphically illustrates the effect of the engine's speed on theparticulates' size distribution;

FIGS. 10-12 are graphically illustrations of particles trajectories.Particle's grouping is well observed for β<1: as β increases, thegrouping tendency is weakened;

FIG. 13 graphically illustrates an approximated benchmark sketch fordesigning a converging pipe design, according to the present invention;

FIG. 14 schematically illustrates an experimental setup having theexhaust of a Diesel engine operatively attached, in parallel, to astraight conventional steel pipe and to a cyclic exhaust pipe, accordingto preferred variations of the present invention, whereas the cyclicexhaust pipe is disposed in vertical direction;

FIG. 15 graphically illustrates an example showing the changes in themass fraction as a function of the particle's diameter while flowinginside the exhaust-pipe shown in FIG. 14; and

FIG. 16 graphically illustrates an example case to show thecharacterization of grouping as a function of the EXHAUST angle.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Before explaining embodiments of the invention in detail, it is to beunderstood that the invention is not limited in its application to thedetails of construction and the arrangement of the components set forthin the host description or illustrated in the drawings. Unless otherwisedefined, all technical and scientific terms used herein have the samemeaning as commonly understood by one of ordinary skill in the art towhich the invention belongs. The methods and examples provided hereinare illustrative only and not intended to be limiting.

A principle intention of the present invention includes providing anexhaust-pipe for a fuel burning engine including a hollow body having aninternal surface, an external surface, a first open end and a secondopen end. The internal surface is shaped to form a standing wave havingat least 2 cycles. When gas containing inhalable particles enters theexhaust pipe through the first open end and flows out of the exhaustpipe through the second open end, a substantial amount of inhalableparticles are grouped to form filterable particles, while flowing insidethe exhaust pipe.

An aspect of the present invention is to provide a new concept ofgrouping in a pipe having a standing wave geometry, which defines avelocity standing wave. When a particle is moving in an oscillatinggas-flow, the particle encounters areas where the velocity of the gas isfaster or slower than the particle's own velocity. The time which takesfor the particle to adjust to the local velocity change depends on thesquare of its diameter. Hence, some particles are affected more thanothers depending on the size of the particles. When a line of evenlydistributed particles enters the pipe, a velocity wave is applied to theparticles. Small delay time, that characterizes sub-micron particles,lead to the situation where a particle is accelerated or decelerateddepending on the position of the particle in that wave (with respect tothe local velocity level).

This brings to the separation between two particles which were movingone after the other, as one is accelerated relative to the other. Theseparation between neighboring particles forms groups. A graphicalexample is illustrated in FIG. 1, where particle trajectories arepresented. At time=0 the particles are evenly distributed downstream onX, and as time passes, two groups are formed.

A standing velocity wave in a pipe is formed by periodically diametervariation downstream. According to the conservation of mass, in asmaller cross section higher velocity is obtained and vice versa. Hence,when the pipe diameter is converging and diverging periodically, astanding wave of velocity is obtained, wherein at any given time, thelocation of the maximum and minimum velocity values will be fixed alongthe pipe. Hence, in such a pipe, particles will experience accelerationand deceleration depending on their location.

Reference is now made to FIG. 2, which is a cross section illustrationof an example exhaust-pipe 100, according to embodiments of the presentinvention. Exhaust-pipe 100 includes a hollow body having internalsurface 120, external surface 110, a first open end 130 and a secondopen end 140. Internal surface 120 is shaped to form standing wavegeometry having at least 2 cycles C. In the example shown in FIG. 1,exhaust-pipe 100 includes 5 cycles C. Reference is also made to FIG. 4a, which schematically illustrates the grouping of particles as afunction of the particle's flowing speed changes inside exhaust-pipe100, and to FIG. 4 b, which graphically illustrates the sinusoidalchange in the particles flow speed over time, while flowing insideexhaust-pipe 100. The values of flow velocity are indicated by thelength of the arrows. The particles are introduced from the inlet withinan oscillating gas-flow. The gas-flow has also a downstream periodicvariation. As the particles travel downstream, grouping takes place andinhalable particles 22 vanish at the expense of size-increase offilterable particles 182.

When gas 20 containing inhalable particles 22 enters exhaust pipe 100through first open end 130 and flows out of exhaust pipe 100 throughsecond open end 140, a substantial amount of inhalable particles 22 aregrouped to form filterable particles 182. It should be noted that someinhalable particles 22 are grouped with larger particles 182, which arefilterable to begin with. For example, using exhaust pipe 100 for avehicle engine, leads to clustering of inhalable particles 22 moving inpipe 100. It should be noted that internal surface 120 is substantiallysymmetric with respect to longitudinal axis 150. Preferably, with nolimitations on other shapes, exhaust pipe 100 has a circular crosssection, as shown in FIG. 3 a. FIG. 3 b shows an example of anelliptical cross section of exhaust pipe 100. The narrow radialdimension D_(N) of the cyclic wave is substantially smaller than thewide radial dimension D_(W) of the wave, wherein the ratio D_(K)/D_(N)directly influences the grouping tendency of submicron particles.

Example

An experimental setup is shown in FIG. 5. The exhaust of a Diesel engine30 is operatively attached, in parallel, to two exhaust pipes: a)straight conventional steel pipe 40, and b) exhaust pipe 100, having 6cycles C. Both pipes 40 and 100 are 80 cm long and have the same flowrate. At the outlet of each pipe measurement apparatus 50 are used tomeasure the size distribution of the particles. A particulate analyzer50 is used to detect and measure particles in the 300 nm to 2 μmdiameter range. Pipe selector 160 is used to select the exhaust pipebeing under test.

The experimental engine specifications are as follows:

Engine model Mitsubishi S3L engine Engine type Three-cylinder, 4-stroke,compression- ignited, air-cooled engine Cylinder stroke/bore stroke/bore78.5/78 mm Displacement volume 1,125 cm³ Rated power: 11.8 kW at 1,500rev/min

In each test, the engine was operated under a set of operationconditions (engine speed and engine load). The engine was run under thespecified conditions to attain steady-state operation, and then theexhaust gas was sampled first from the regular pipe and subsequentlyfrom the resonating pipe. Each sample was averaged during a timeinterval of 30 seconds.

The results show a considerable decrease of the amount of the smallerparticles at the expense of larger mass in the larger particlesize-section. FIG. 6 graphically illustrates the decrease of the amountinhalable particles flowing out of exhaust pipe 100 compared with theinhalable particles flowing out of straight pipe 40.

The effect of exhaust pipe 100 is clearly demonstrated in FIG. 7, whichis a graphically illustration of the effect of cyclic exhaust pipe 100,according to embodiments of the present invention, on the particulates'size distribution. The example setup is as follows: engine speed=1,700rpm, engine load=0 kW, exhaust pipe 100 aspect ratio, D_(W)/D_(N)=2.27,length to diameter ratio, L/D=2.0. FIG. 7 shows how the sizedistribution of the exhaust particles is affected. The mass fractionchange Δmass fraction is defined as follows:

Δmass_fraction=M _(modified) −M _(reg),

Where M_(modified) is the mass of larger particles 182, measured at theexhaust of cyclic exhaust pipe 100, and M_(reg) is the particles massmeasured at the exhaust of regular pipe 40.

The apparent mass fraction of small particles 22 (in particular, in thesub-micron regime) has been reduced by some 2-6%, whilst the massfraction of larger particles 182 was increased by some 1-2%. Whileparticles 22 smaller than 0.3 μm are not detectable by the particulatesize analyzer used, mass conservation suggests that the remarkableincrease in the mass fraction of the larger-size particles 182, mayconfidently be attributed to the grouping (leading to agglomeration) ofthe undetected smaller-size particles 22. Similar encouraging resultswere observed in a wide range of engine loads (FIG. 8) and engine speeds(FIG. 9).

The effect of the engine load at 1,700 rpm is depicted in FIG. 8, whichis a graphically illustration of the effect of the engine's load on theparticulates' size distribution. Although, when the engine loadincreases, the total number of particles in any particle-size categoryincreases as well, the effect of the alternating diameter pipe is fairlycomparable.

FIG. 9 shows the effect of the engine speed on the mass fraction changeat an engine load of 2 kW. The results for the 1,500 rpm and 1,700 rpmare quite similar to those shown earlier. The results for the 1,900 rpmstill show the migration of inhalable particles 22 towards larger-sizeparticle 182, but the effect is rather mild. It should be noted that thetotal amount of the particles is low due to the low engine load, whilethe residence time of the particles in the exhaust pipe is relativelyshort due to the high exhaust gas velocity.

Mathematical Analysis of Grouping in a Converging Pipe (Standing WaveVelocity Field)

The converging pipe geometry induces particle grouping and coagulationleading to a shift in particle size distribution, which increases themass/number of the larger particles at the expense of the reduction inthe amount of smaller particles.

The velocity field U inside pipe 100 is a standing wave velocity fieldwith modification:

U=U _(a) −U _(b) cos(kx)(sin(ωt)+C),  (1)

where U_(a) is the mean velocity, C is constant, U_(b) is the amplitude,w is the angular frequency of the wave (

$\omega = \frac{2\pi}{T}$

where T is the wave period) and k is the wave number (

$k = \frac{2\pi}{L}$

where L is the wave length).

The constant C is introduced in order to achieve the maximal and minimalvelocity values at the areas of biggest and smallest diameter,correspondingly, and C>1 to fulfill that condition.

The equation of particle motion in a dimensional form is:

$\begin{matrix}{\overset{¨}{x} = \frac{1}{\tau_{p}\left( {U - \overset{.}{x}} \right)}} & (2)\end{matrix}$

where x is the particle location and

$\tau_{p} = {\frac{1}{18}\frac{\rho_{p}D_{p}^{2}}{\mu}}$

(Katoshevski, D., Dodin, Z., Ziskind, G., 2005, “Aerosol clustering inoscillating flows: mathematical analysis”, Atomization and Sprays 15,401-412), ρ_(p) is the particle density, D_(p) is the particle diameter,and μ is the dynamic viscosity of the host gas.

Substituting the velocity field (Eq. 1) into the particle equation ofmotion (Eq. 2) leads to the following dimensional equation:

$\begin{matrix}{{{\overset{¨}{x} + {\frac{1}{\tau_{p}}\overset{.}{x}} + {\frac{U_{b}}{\tau_{p}}{\cos ({kx})}\left( {{\sin \left( {\omega \; t} \right)} + C} \right)}} = \frac{U_{a}}{\tau_{p}}},} & (3)\end{matrix}$

The normalized velocity field is:

U*=U* _(a) −U* _(b) cos(x*)(sin(t*)+C),  (4)

where the velocities are normalized with a characteristic velocity:U_(c), where U_(c)=ω/k. x is normalized with k and t with ω (theasterisk denotes dimensionless parameters).

The equation of particle motion in dimensionless form is:

$\begin{matrix}{{\overset{¨}{x}}^{*} = {\frac{1}{St}\left( {U^{*} - {\overset{.}{x}}^{*}} \right)}} & (5)\end{matrix}$

where x* is the particle location and

${St} = {\frac{1}{18}\frac{\rho_{p}\omega \; D_{p}^{2}}{\mu}}$

is the Stokes number.

Inserting the dimensionless velocity field into the particle equation ofmotion leads to the following equation:

$\begin{matrix}{{{{\overset{¨}{x}}^{*} + {\frac{1}{St}{\overset{.}{x}}^{*}} + {\frac{U_{b}^{*}}{St}{\cos \left( x^{*} \right)}\left( {{\sin \left( t^{*} \right)} + C} \right)}} = \frac{U_{a}^{*}}{St}},} & (6)\end{matrix}$

Introducing:

θ=x*−t*

leads to:

$\begin{matrix}{{\overset{¨}{\theta} + {\frac{1}{St}\overset{.}{\theta}} + {\frac{U_{b}^{*}}{St}{\cos \left( {\theta + t^{*}} \right)}\left( {{\sin \left( t^{*} \right)} + C} \right)}} = \frac{U_{a}^{*} - 1}{St}} & (7)\end{matrix}$

Introducing:

$t^{*} = \frac{\tau}{\sqrt{U_{b}^{*}/{St}}}$

leads to:

{umlaut over (θ)}+{dot over (θ)}+α cos(θ+t*)[sin(t*)+C]=β,  (8)

where

$\begin{matrix}{{\alpha = \frac{1}{\sqrt{{StU}_{b}^{*}}}}{and}} & (9) \\{\beta = {\frac{\left( {U_{a}^{*} - 1} \right)}{U_{b}^{*}}.}} & (10)\end{matrix}$

In order to ensure grouping we need to maintain β<1.

There are basically two modes of grouping, where one is denoted as“stable grouping” and the other is denoted as “non-stable grouping”. Inthe stable mode, particles are forming groups that do not brake furtherdownstream. In the non-stable mode, groups may breakup and some of theparticles do not group at all. In order to ensure a high degree ofgrouping or stable grouping, the condition of β<1 has to besubstantially fulfilled. Smaller particles (typically smaller than 80μbut larger than a molecule), having a diameter close to zero, have ahigher tendency to group, that is smaller Stokes number. However, toensure grouping the condition β<1 should be fulfilled, although groupingin the standing wave configuration may occur also at β<1.

FIGS. 10-12 demonstrates calculations for particle trajectories asmeasured on example system 200 shown in FIG. 5. Three sets ofcalculations are made with the same value of C (C=1.5) but withdifferent β values (β=0.4, 0.94, 2.4). Particle diameters are set to 0.3μm and 1.5 μm, sizes which are relevant to the experimental resultsdescribed in FIGS. 10-12. Particles groups after approximately 2 cyclesare shown in FIGS. 10-12. Grouping is denoted by the dense area of FIG.10 where the trajectories of the particles come closer together. As β isincreased from 0.4 to 0.94 the tendency for grouping is decreased asshown in FIG. 11 (the lines are less dense) and for a larger value of β,2.4, as shown in FIG. 12, the situation may be denoted as weak groupingor non-grouping. This coincides with the results mentioned earlier,obtained for the moving wave scenario, that is, β should be less thanunity to ensure a significant degree of grouping. It is important tonote that the model does not include a “sticking” factor, and, as sootparticles do have some stickiness characteristics, practically, asignificant coagulation takes place after 2 wave lengths and continuedownstream exhaust-pipe 100, having standing wave geometry.

Following the above condition as a design tool for converging pipe 100,β is defined with the following parameters of converging pipe 100:

A_(max) Maximum area of the pipe A_(min) Minimum area of the pipe fFrequency of pulsating flow at inlet L Distance between two nodes NEngine speed in rev/min n Number of cylinders Q Volumetric flow rate RArea ratio (A_(max)/A_(min)) V_(d) Cylinder displacement volume (for onecylinder) x Engine revolutions per working stroke (=2 for 4 strokeengine)

Let us define, for convenience, T=sin(ωt)+C. Applying mass conservationbetween maximum and minimum locations and assuming that the density ofthe gas is constant.

$\begin{matrix}{\frac{U_{a} + {U_{b}T}}{U_{a} - {U_{b}T}} = \frac{A\; \max}{A\; \min}} & (11)\end{matrix}$

Inserting to β and using dimensional expressions:

$\begin{matrix}{\beta = {\frac{U_{a} - \frac{\omega}{k}}{U_{b}} = {2\frac{U_{a} - \frac{\omega}{k}}{\frac{U_{a}}{T}\frac{\left( {{A\; \max} - {A\; \min}} \right)}{\left( {{A\; \min} + {A\; \max}} \right)}}}}} & (12)\end{matrix}$

Using the relations:

${Q = {\frac{N \cdot n}{60 \cdot x}V_{d}}},{f = \frac{N \cdot n}{60 \cdot x}}$

we can write:

$\begin{matrix}{\frac{\omega}{k} = {{fL} = {\frac{Q}{V_{d}}L}}} & (13)\end{matrix}$

Inserting that to β:

$\begin{matrix}{\beta = {T\left( {1 - {2\frac{\left( {V^{*} - 1} \right)}{\left( {R - 1} \right)}}} \right)}} & (14)\end{matrix}$

where T is a function of time, and in order to evaluate its value weshould relate time to the grouping occurrence. This is enabled by usingthe mathematical model as reflected in FIGS. 10-12.

The characteristic grouping time is related to the value of β, whichfacilitates a practical design tool of the exhaust pipe, as described inFIG. 13, which is a benchmark sketch for design. That sketch enables toevaluate the pipe-geometry as a function of engine characteristics. Foroptimal performance it is suggested that 0<β<1. For example, the valueof the volume ratio V* for the example system 200, shown in FIG. 5, is0.62, and the cross section area relation is R=5.14. For the case ofβ=0.94, described in FIG. 11, the corresponding value of the function T(Eq. 14) leads to the time value of 0.025 sec. This in turn correspondswell to the grouping occurrence as reflected in FIG. 11. Hence, fixingthe correct position of the curve for V*=0.62 in that sketch.

In preferred variations of the present invention, exhaust pipe 100 isoperatively disposed vertically, whereas the internal flow of gas isgenerally upwardly. Reference is made to FIG. 14, which schematicallyillustrates an experimental setup 300 having the exhaust of a Dieselengine 30 operatively attached, in parallel, to a straight conventionalsteel pipe 40 and to a cyclic exhaust pipe 100, according to preferredvariations of the present invention, whereas cyclic exhaust pipe 100 isdisposed in vertical direction. Both pipes 40 and 100 are 80 cm long andhave the same flow rate. At the outlet of each pipe measurementapparatus 50 are used to measure the size distribution of the particles.Hence, disposing cyclic exhaust pipe 100 is disposed in verticaldirection, wherein a first open end 130 is pointing upwardly.

The results show a considerable decrease of the amount of the smallerparticles at the expense of larger mass in the larger particlesize-section, compared with setup of system 200, shown in FIG. 5,operated under substantially the same conditions.

FIG. 15 graphically illustrates an example showing the changes in themass fraction as a function of the particle's diameter while flowinginside the exhaust-pipe 100 being part of system 300, wherein the engineoperates at 1500 rpm and with a 6 kW load. It should be noted that thegrouping rate can by characterized by the slope denoted by angle θ. Thelarger angle θ is, the higher the grouping rate is. FIG. 16 graphicallyillustrates an example case to show the characterization of grouping asa function of angle θ, at various engine speeds.

In other variations of the present invention, exhaust pipe 100 isoperatively disposed diagonally, whereas the internal flow of gas isgenerally upwardly.

It should be noted that the resistance pressure inside a conventionalexhaust pipe 40 and compatible exhaust pipe 100 are substantially thesame.

The invention being thus described in terms of embodiments and examples,it will be obvious that the same may be varied in many ways. Suchvariations are not to be regarded as a departure from the spirit andscope of the invention, and all such modifications as would be obviousto one skilled in the art are intended to be included within the scopeof the claims.

1. An exhaust pipe for a fuel burning engine comprising a hollow body,said body having an internal surface, an external surface, a first openend, a second open end and a longitudinal axis, wherein said internalsurface is shaped to form standing cyclic wave geometry having at least2 cycles; and wherein gas containing inhalable particles that enters theexhaust pipe through said first open end and flows out of the exhaustpipe through said second open end, wherein a substantial amount of saidinhalable particles are grouped to form filterable particles whileflowing inside the exhaust pipe.
 2. The exhaust pipe of claim 1, whereinsaid longitudinal axis is disposed horizontally.
 3. The exhaust pipe ofclaim 1, wherein said longitudinal axis is disposed vertically, whereinsaid second open end is elevated with respect to said first open end. 4.The exhaust pipe of claim 1, wherein said longitudinal axis is disposeddiagonally, wherein said second open end is elevated with respect tosaid first open end.
 5. The exhaust pipe of claim 1, wherein saidstanding cyclic wave includes a narrow radial dimension D_(N) and a wideradial dimension D_(W), wherein said narrow radial dimension D_(N) issubstantially smaller than said wide radial dimension D_(W).
 6. Theexhaust pipe of claim 5, wherein the ratio D_(W)/D_(N) directlyinfluences the grouping tendency of submicron particles.
 7. The exhaustpipe of claim 1, wherein the cross section of the exhaust pipe can beradial, polygonal, elliptical or other shapes.
 8. The exhaust pipe ofclaim 1, wherein the velocity field U inside the exhaust pipe is astanding wave velocity field:U=U _(a) −U _(b) cos(kx)(sin(ωt)+C), where U_(a) is the mean velocity, Cis constant, U_(b) is the amplitude, ω is the angular frequency of thewave: $\omega = \frac{2\pi}{T}$ where T is said wave period, and k issaid wave number: $k = \frac{2\pi}{L}$ where L is said wave length; andwherein said constant C is selected to achieve the maximal and minimalvelocity values at D_(W) and D_(N), respectively.
 9. The exhaust pipe ofclaim 8, wherein the normalized velocity field U* is:U*=U* _(a) −U* _(b) cos(x*)(sin(t*)+C), where the velocities arenormalized with a characteristic velocity: U_(c), where U_(c)=ω/k; x isnormalized with k and t with w, and wherein the asterisk denotesdimensionless parameters; and wherein substantial grouping occurs when:$\frac{\left( {U_{a}^{*} - 1} \right)}{U_{b}^{*}} < 1.$